Adjusted Goal Differential

This is a new type of analysis I've been working on. Due to the nature of hockey the amount of goals scored for and against depends on who you play against. If a team played the entire NHL season against Minnesota, Dallas and Vancouver, San Jose, New Jersey and Detroit they would score significantly fewer goals compared to a schedule that only included Philadelphia, Boston, Washington, Phoenix and L.A.

Generally the basic principle in hockey is individual game scoring rate = GF₁*GA₂/League average. So if all the teams you play have a high GA₂, then you'll have a higher scoring rate even if your GF₁ is low.

This system looks at every game played and calculates all the GF_x, GA_x simultaneously.
GF_i - Goals for/Hr for team i.
GA_i - Goals against/Hr for team i.
TGF_i - Total Goals for/Hr for team i.
TGA_i - Total Goals against/Hr for team i.

Now I know how many goals each team has scored for and against, or the TGF and TGA values, but the GF and GA rates are unknown. Generally they are estimated by simply calculating a basic TGF/icetime, however if opponents are better or worse defensively this method wont work to calculating a true GF rate that is independent of opposition. Each team has two equations, which are displayed below and two unknowns (GF_i, GA_i). These equations are non-linear and another constraint is added to keep the rates consistent with what we typically see in hockey. The extra constraint is just that: Average(GF_i)= Average(GA_i)=league average goals for rate = 2.83 GF/Hr. I ignored empty net goals and 4th period goals.


In accordance to, "Games 1-20 are effectively ancient history" so I excluded the first 20 or so games.

Results

The first column on the left displays 2006 playoff team's results and is color coded so that the teams who are out in the first round are 'struck out'. Teams who make it to the second round are in bold. Teams who make it to the third are green. Playoff teams are darker green and the Stanley cup winner is very dark green with white text. The other column are the results for 2007.

I find it interesting that Buffalo appears fallible by this method. Like any method like this, the South East division looks like crap. Every series in the west is reasonably close.